Hello dear,
I'm sorry you're going through this. I'm going to be a first time mom this year (12weeks now). Let me start by saying that we don't have any complications as of now but here is what we are doing. We told the closest family/friends but decided not to make it public until we are done with genetical testing. We should have the results by next week. If there are any issues we decided that we will get to the bottom of them and once all is known to us then we will share with the rest of family/friends that we feel comfortable with. Either way we won't go out screaming that we are expecting. We will keep it more intimate.
From what I know, sometimes there could be another issue if the omphalocele is present. If I were you I'd probably first get to the bottom of things to see what you're actually dealing with.
I also heard that omphalocele at times diminishes or goes away with weeks of pregnancy. I also read that often it is fairly easy to fix after birth.
One more thing...it is your Baby, and either way it IS a very happy news!!
That's jus my opinion. I wish you strength and peace.